How to twist a cloth?
Probably not serious answer, but easier to explaine. What about to add one collision object?

Example with only one bone (your blend) plus Cylinder as collider, bad timing and probably better to use some less circle shape, but you got idea.





For final shape you can try Modeling Cloth addon, you can "model" shape in a realtime, final shape is stored as shapekey. So no way to just do animation with two shapekeys O-1, the transition wouldn't work for you.

You can try some combination of your baked cloth sim + shapekey from this addon, somehow ... export to MMD, assign to a mesh via Mesh Cache works, than I wanted to use Surface Deform modifier after that (for target object shaped in state of end of simulation with adjustments as shapekey), but they doesn't run together.

It's really hard to understand how ideal result should looks like :)